Finite Group Databasebeta

← #14739222

Subgroups — #14739222

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079568C211yesmaximal, characteristic, complemented
2#13078767C211yesmaximal, characteristic
3#13077727C211yesmaximal, characteristic, complemented
4#13068062C211yesmaximal, characteristic, complemented
5#13068055C211yesmaximal, characteristic, complemented
6#13068048C211yesmaximal, characteristic, complemented
7#13068041C211yesmaximal, characteristic, complemented
8#13067984C211yesmaximal, characteristic, complemented
9#13067979C211yesmaximal, characteristic, complemented
10#13067966C211yesmaximal, characteristic, complemented
11#13067959C211yesmaximal, characteristic, complemented
12#13067394C211yesmaximal, characteristic, complemented
13#13067316C211yesmaximal, characteristic, complemented
14#13067263C211yesmaximal, characteristic, complemented
15C11×#3107C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#485—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#462C2211yescharacteristic
23C11×#461C2211yescharacteristic
24C11×#452—21no—
25C4×C11×Q16—21no—
26C4×C11×SD16—21no—
27C11×#431C2211yescharacteristic
28#10622851—21no—
29#10622706C2211yescharacteristic
30#10622705C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622698C2211yescharacteristic
33#10622660—21no—
34#10622660—21no—
35#10622641—21no—
36#10622641—21no—
37#10622640C2211yescharacteristic
38#10622639—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622628C2211yescharacteristic
43#10622627—21no—
44D4×C11⋊C8—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622616—21no—
50#10622539C2211yescharacteristic
51#10622538—21no—
52#10622538C2211yescharacteristic
53C2×C4⋊(C11⋊C8)—21no—
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622123C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#125—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11D411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117—21no—
86C11×#117D411yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4326—21no—
90C2×#4326—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4323—21no—
95#66983—21no—
96#66983—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8—21no—
100#66928—21no—
101#66927C2311yescharacteristic
102C4×D44—21no—
103C4×D44—21no—
104#66922C2311yescharacteristic
105C11×#107—21no—
106C11×#106—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C4×C8×C11—21no—
115#66899—21no—
116#66896—21no—
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)D411yescharacteristic
121C22⋊(C11⋊C8)D411yescharacteristic
122#66874—21no—
123#66874—21no—
124#66873—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)D411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19413—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×C22⋊D11—41no—
159#4339—81no—
160#4339—81no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×C4×D11—41no—
165C2×Dic22—21no—
166C11×Q16—42no—
167C11×SD16—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—41no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4326—81no—
193#4326—81no—
194#4325—42no—
195#4325—81no—
196#4325—81no—
197#4323—42no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3210—111no—
214#3115—111no—
215#3107D1111yescharacteristic, complemented
216#2988—111no—
217#1682—111no—
218#1681—111no—
219#1680—111no—
220#1679—111no—
221#1670—111no—
222#1669—111no—
223#1666—111no—
224#1665—111no—
225#1572—111no—
226#1552—111no—
227#1540—111no—
228C23×C11—21no—
229C23×C11#12111yescharacteristic
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11#13512yes—
237D4×C11—24no—
238D4×C11—21no—
239D4×C11#13512yes—
240C2×C4×C11—24no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—81no—
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C22⋊D11—82no—
261C2×Dic11—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—81no—
267C4×D11—82no—
268Dic22—41no—
269Dic22—41no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#533C2×D1111yescharacteristic
281#532—111no—
282C4×#41C2×D1111yescharacteristic
283#494—111no—
284#492—111no—
285#487—111no—
286#486—111no—
287#485—21no—
288#482—221no—
289#475—111no—
290#475C2×D1111yescharacteristic
291#474—111no—
292#474C2×D1111yescharacteristic
293#464—221no—
294#464—221no—
295#462C2×D1111yescharacteristic
296#461C2×D1111yescharacteristic
297#460—111no—
298#459—111no—
299#452—21no—
300#452—221no—
301#452—221no—
302#449—221no—
303C8×Q8—111no—
304C8×Q8—111no—
305#442—221no—
306#440—221no—
307C4×Q16—21no—
308C4×SD16—21no—
309C8×D4—111no—
310C8×D4—111no—
311C8×D4—221no—
312C8×D4—221no—
313#432—111no—
314#431—111no—
315#431—221no—
316#431C2×D1111yescharacteristic
317C2×C4⋊C8—111no—
318C2×C4⋊C8—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#331—111no—
330#331—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—22no—
334C22×C11—21no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×#12111yescharacteristic
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11C2×#13511yescharacteristic
351C4×C11C2×#13511yescharacteristic
352C4×C11#57611yescharacteristic
353C4×C11#57711yescharacteristic
354Dic11—81no—
355C2×#41—221no—
356C2×#41C22⋊D1111yescharacteristic
357C2×Q16—21no—
358C2×Q16—221no—
359C2×Q16—221no—
360C2×SD16—21no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×D8—221no—
365C22×C8—221no—
366C22×C8—221no—
367C22×C8—221no—
368C4⋊Q8—111no—
369C4⋊Q8C22×D1111yescharacteristic
370C4⋊Q8C22×D1111yescharacteristic
371#127—111no—
372#125—21no—
373#124—221no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—221no—
377#121—221no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C22⋊D1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—221no—
385C4×D4—221no—
386C4×D4C22⋊D1111yescharacteristic
387C4×D4C22×D1111yescharacteristic
388#117—21no—
389#117—21no—
390#117C22⋊D1111yescharacteristic
391C2×C42—21no—
392C2×C42C22×D1111yescharacteristic
393#107—21no—
394#107—221no—
395#106—21no—
396#106—221no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—221no—
412#103—221no—
413#103—221no—
414#102—21no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—21no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426#97—221no—
427C4×C8—21no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—221no—
431C4×C8—221no—
432C2×C11—41no—
433C2×C11—42no—
434C2×C11#304511yescharacteristic
435C2×C11#305011yescharacteristic
436C2×C11#306911yescharacteristic
437D11—161no—
438#41—22no—
439#41—22no—
440#41—881no—
441#41—881no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—221no—
445C2×Q8C2×C22⋊D1111yescharacteristic
446C2×D4—21no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—441no—
451C2×D4C2×C22⋊D1111yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—441no—
456C22×C4D4×D1111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—42no—
460Q16—881no—
461Q16—881no—
462SD16—42no—
463SD16—442no—
464SD16—881no—
465SD16—881no—
466D8—442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—881no—
478C2×C8—881no—
479C2×C8—881no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4C2×C22⋊D1111yescharacteristic
491C4⋊C4C2×C22⋊D1111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42D4×D1111yescharacteristic
503C42#434111yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1941311yescharacteristic, complemented, Sylow
507C23—21no—
508C23—441no—
509C23#6699211yescharacteristic
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—441no—
516Q8—441no—
517Q8#6700312yes—
518D4—24no—
519D4—21no—
520D4—441no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—881no—
525D4—882no—
526D4#6700312yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—81no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4#6699211yescharacteristic
544C2×C4#6699211yescharacteristic
545C2×C4#6699211yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4C2×#434111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—41no—
550C8—41no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—221no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8—441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22C2×#6699211yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—881no—
579C4#1062330011yescharacteristic
580C4#1062330111yescharacteristic
581C4C2×#6700311yescharacteristic
582C4C2×#6700311yescharacteristic
583C2—41no—
584C2—42no—
585C2—1761no—
586C2#1307815311yescharacteristic
587C2#1307819411yescharacteristic
588C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3107C2
socleC22×C11C2×#121
prime radical#13078767C2
hypercenter#3107D11
hypocenterC11#19413
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13079568C2semidirect
3. #13077727C2semidirect
4. #13068062C2semidirect
5. #13068055C2semidirect
6. #13068048C2semidirect
7. #13068041C2semidirect
8. #13067984C2semidirect
9. #13067979C2semidirect
10. #13067966C2semidirect
11. #13067959C2semidirect
12. #13067394C2semidirect
13. #13067316C2semidirect
14. #13067263C2semidirect
15. C11×#3107C2semidirect
215. #3107D11semidirect
506. C11#19413semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130795682
#130787672
#130777272
#130680622
#130680552
#130680482
#130680412
#130679842
#130679792
#130679662
#130679592
#130673942
#130673162
#130672632
C11×#31072
#1941311